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A323350
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Nonprime numbers > 1 whose number of prime factors counted with multiplicity is a perfect square.
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2
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16, 24, 36, 40, 54, 56, 60, 81, 84, 88, 90, 100, 104, 126, 132, 135, 136, 140, 150, 152, 156, 184, 189, 196, 198, 204, 210, 220, 225, 228, 232, 234, 248, 250, 260, 276, 294, 296, 297, 306, 308, 315, 328, 330, 340, 342, 344, 348, 350, 351, 364, 372, 375, 376
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OFFSET
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1,1
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COMMENTS
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First differs from A014613 in having 512.
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LINKS
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EXAMPLE
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360 = 2*2*2*3*3*5 has 6 prime factors, and 6 is not a perfect square, so 360 does not belong to the sequence.
2160 = 2*2*2*2*3*3*3*5 has 8 prime factors, and 8 is not a perfect square, so 2160 does not belong to the sequence.
10800 = 2*2*2*2*3*3*3*5*5 has 9 prime factors, and 9 is a perfect square, so 10800 belongs to the sequence.
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MAPLE
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filter:= proc(n) local t;
t:= numtheory:-bigomega(n);
t > 1 and issqr(t)
end proc:
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MATHEMATICA
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Select[Range[100], #>1&&!PrimeQ[#]&&IntegerQ[Sqrt[PrimeOmega[#]]]&]
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PROG
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(PARI) isok(n) = (n>1) && !isprime(n) && issquare(bigomega(n)); \\ Michel Marcus, Jan 15 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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